Percent Change Calculator
Find the percent change between any two numbers — with every step shown. Includes a reverse percent change solver (recover the original value), a sequential changes mode (why +20% then −15% is not +5%), and honest handling of zero and negative numbers.
🔒 100% client-side — your numbers never leave this browser.
Three calculators in one
The formulaThe Percent Change Formula — Show Your Work
In words: new minus old, divided by old, times one hundred. The sign of the answer tells the story — positive means the value went up, negative means it went down, zero means nothing changed.
Why the absolute value in the denominator? When the old value is negative, dividing by a plain negative flips the sign of the answer backwards. Using |old value| keeps the sign honest: moving toward zero from −50 to −25 is a genuine +50% improvement, and moving away from zero from −50 to −75 is a genuine −50% decline. Every calculator on this page uses this convention, and the methodology section below documents it.
DirectionPercent Increase vs Percent Decrease
There is no separate formula for increases and decreases — they are the two halves of one signed number. If the result is positive, call it a percent increase; if negative, a percent decrease (report the magnitude: −25% is "a 25% decrease").
| Old → New | Percent change | How to say it |
|---|---|---|
| 50 → 75 | +50% | a 50% increase |
| 80 → 60 | −25% | a 25% decrease |
| 25 → 75 | +200% | tripled (a 200% increase) |
| 80 → 0 | −100% | fell to zero (a 100% decrease) |
| 40 → 40 | 0% | no change |
A decrease can never be "more than 100%" — −100% already means the value hit zero. An increase has no ceiling: +200% means tripled, +900% means ten times the original.
Reverse solverReverse Percent Change, Explained
Sometimes you know the after and the percent, and need the before — a sale price after 20% off, a salary after a 16% raise, a population after 8% growth. That is just the formula solved backwards:
Example: after a 25% increase a price is $250. The original was 250 ÷ 1.25 = $200. The Reverse Solver tab above does both directions and shows the working. One honest limit: a −100% change erases the original value completely, so there is nothing to recover — the solver says so instead of inventing a number.
CompoundingSequential Percent Changes (Why +20% Then −15% ≠ +5%)
Percent changes multiply; they never add. Each step applies to the result of the previous one, not to the original:
The naive answer (+5%) overstates the result by two and a half times. The Sequential Changes tab chains up to 10 steps, shows each factor and the running total, and — if you enter a starting value — the final number. Year-over-year growth, multi-stage discounts, and investment returns all work this way.
Don't confuse themPercent Change vs Percent Difference
These two are constantly mixed up, but they answer different questions:
| Percent change | Percent difference | |
|---|---|---|
| Formula | (new − old) ÷ |old| × 100 | |a − b| ÷ average(a, b) × 100 |
| Direction | Directional (old → new) | Symmetric (order doesn't matter) |
| Sign | Signed: + or − | Always positive |
| Example 50, 75 | +50% | 40% |
| Use when | Before/after: prices, weight, revenue, growth | Neither is the "start": comparing two measurements, experimental vs theoretical |
Related but separate intents also live on their own pages: percent increase (growth-only framing) and the reverse solver above covers the "find the original" intent in one place.
Common trapPercent Change vs Percentage Points
If an interest rate moves from 4% to 6%, it rose by 2 percentage points — the plain arithmetic gap. The percent change is (6 − 4) ÷ 4 × 100 = +50%: relative to where it started, the rate is half again as large. News headlines mix these up constantly ("rates up 50%" vs "rates up 2 points" describe the same move). When both your inputs are percentages, tick "Both values are percentages" in the calculator to see both numbers side by side.
Edge casesPercent Change With Negative Numbers & Zero
Negative starting values. Dividing by |old| keeps the sign meaningful: −50 → −25 is +50% (the value improved toward zero), −50 → −75 is −50% (it worsened). Crossing zero works too: −20 → 30 is +250%. Many thin calculators divide by the raw negative and report nonsense signs; this one doesn't.
Zero starting value. Percent change from 0 is undefined — division by zero, no way around it. From 0 to 5 is not "500%" or "infinite%"; it is simply not a percent change at all, because there is no baseline to be relative to. The calculator shows an honest error. (The single defined case: 0 → 0 is 0%, no change.) In Excel, wrap your formula: =IF(A2=0,"n/a",(B2-A2)/ABS(A2)).
SpreadsheetsPercent Change in Excel & Google Sheets
With the old value in A2 and the new value in B2:
= (B2 - A2) / ABS(A2) → format the cell as % = IF(A2 = 0, "n/a", (B2 - A2) / ABS(A2)) → zero-safe version
In Google Sheets the identical formulas work. For a pivot table, add a calculated field with the same expression; for a chart, compute the column first — charts can't do the division themselves. A common shortcut — =B2/A2-1 — is the same math in disguise.
Worked examplesThree Examples, Step by Step
1. Price rise: $32 → $60
- Difference: 60 − 32 = 28
- Divide by old: 28 ÷ 32 = 0.875
- × 100 → +87.5% increase
2. Small dip: 96 → 93
- Difference: 93 − 96 = −3
- Divide by old: −3 ÷ 96 = −0.03125
- × 100 → −3.125% (a 3.125% decrease)
3. Salary raise: $50,000 → $58,000
- Difference: 58,000 − 50,000 = 8,000
- Divide by old: 8,000 ÷ 50,000 = 0.16
- × 100 → +16% raise
In the wildWhere Percent Change Is Used
Daily price moves, portfolio returns, and year-over-year growth are all percent changes.
A $50k → $58k move is a 16% raise — the number that matters in negotiations.
Tracking change relative to your starting weight keeps progress honest.
Sale math is reverse percent change: $96 after 25% off means $128 originally.
Month-over-month and year-over-year growth rates drive every dashboard.
Percent change in mass, population growth, and experiment deltas.
MethodologyHow This Calculator Works
Definition. Percent change = (new − old) ÷ |old| × 100. The denominator uses the absolute value so negative starting values produce correctly-signed results.
Zero baseline. Old value 0 with a nonzero new value is undefined (honest error, not a fabricated number). 0 → 0 is reported as 0%.
Reverse math. New = old × (1 + p/100); old = new ÷ (1 + p/100). A −100% change cannot be reversed (division by zero) and is reported as unrecoverable.
Sequential math. Step factors (1 + p/100) are multiplied, never added; the total is (product − 1) × 100.
Rounding. Results display up to 6 decimal places with float noise trimmed (−0 is normalized to 0). Internal math is full double precision.
Verification. The engine was tested against 56 hand-computed vectors (increases, decreases, negatives, zero edges, reverse round-trips, compound chains) before this page shipped; the test artifacts live with the tool source.
Privacy. Everything runs in your browser. No inputs are sent anywhere — there is literally no server to send them to.
FAQPercent Change Questions, Answered
Percent change = (new value − old value) ÷ |old value| × 100. Subtract the old value from the new value, divide by the absolute old value, then multiply by 100. A positive answer means an increase, a negative answer means a decrease. Example: from 50 to 75 → (75 − 50) ÷ 50 × 100 = +50%.
Take the difference between the two numbers (new minus old), divide that difference by the starting (old) number, and multiply by 100. For example, a price rising from $32 to $60: (60 − 32) ÷ 32 × 100 = 87.5%. The calculator above does this in three modes — direct change, reverse solve, and sequential changes — and shows every step.
Yes. A negative percent change simply means the new value is smaller than the old value — a decrease. From 80 to 60 the percent change is −25%. The sign carries meaning: + means up, − means down. (Percent difference, the symmetric variant, is always reported as a positive number instead.)
Yes. Percent change above 100% means the value more than doubled. From 40 to 120 the change is +200% because the increase (80) is twice the starting value (40). There is no upper cap: tripling is +200%, quadrupling is +300%, and so on. A decrease, however, can never go below −100%, because a value cannot fall below zero and still be expressed this way.
It is undefined — you cannot divide by zero. Any calculator that returns a number for an old value of 0 is making one up, because percent change is always relative to the starting point and there is no starting point to be relative to. This calculator shows an honest error instead. The only defined case is 0 → 0, which is 0% (no change).
Percent change is directional: it measures change from an old value to a new value, divided by the old value — (new − old) ÷ |old|. Percent difference is symmetric: it measures how far apart two values are, divided by their average — |a − b| ÷ ((a+b)/2) — and is always positive. Use percent change for before/after (prices, weight, revenue); use percent difference when neither value is the 'start' (comparing two measurements).
They answer different questions. If an interest rate moves from 4% to 6%, the change is 2 percentage points, but the percent change is +50% ((6−4) ÷ 4 × 100). Percentage points are the simple arithmetic difference of two percentages; percent change is the relative change. Confusing them is one of the most common statistics mistakes in news reporting.
If the old value is in A2 and the new value in B2, use =(B2-A2)/ABS(A2) and format the cell as a percentage. The ABS() protects you when the old value is negative. To guard against a zero starting value, use =IF(A2=0,"n/a",(B2-A2)/ABS(A2)). In Google Sheets the same formulas work unchanged.
Divide by the absolute value of the old number, so the sign of the result always reflects the direction of movement. From −50 to −25 the value moved toward zero (up), giving +50%: (−25 − (−50)) ÷ |−50| × 100. From −50 to −75 it moved away from zero (down), giving −50%. Without the absolute value the signs come out backwards, which is why this convention is standard.
Mostly yes in everyday use — a growth rate is just percent change measured over a time period (year-over-year growth, quarter-over-quarter growth). In economics the terms are used interchangeably. The only nuance is that 'growth rate' sometimes implies compounding over multiple periods, while a single percent change is one step.
Use algebra on the formula. To find the new value: new = old × (1 + p/100). To recover the old value from the new one: old = new ÷ (1 + p/100). For example, after a 25% increase a price is $250, so the original was 250 ÷ 1.25 = $200. One honest limit: a −100% change destroys the original value (division by zero), so it cannot be reversed.
Because percent changes multiply, they never add. A +20% then −15% sequence means ×1.20 × 0.85 = ×1.02, a total of +2% — the second change applies to the already-increased value, not the original. The 'Sequential' tab of the calculator shows the factor chain step by step so you can see exactly where the naive addition goes wrong.
Percent increase is the positive half of percent change. Percent change is the general, signed concept: positive results are increases, negative results are decreases. If you only ever deal with growth, a percent-increase framing is fine; this calculator handles both directions with the sign doing the work.
Same formula, relatable numbers. A salary rising from $50,000 to $58,000: (58,000 − 50,000) ÷ 50,000 × 100 = +16% — that is your raise in percent terms. A price falling from $96 to $93: (93 − 96) ÷ 96 × 100 = −3.125% — a 3.125% discount. The 'values are percentages' option is not needed here; only enable it when both inputs are already percentages and you want the percentage-point gap too.